Crate zernike

Zernike polynomials

Computes the Zernike polynomials according to Noll ordering:

j	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	…
n	0	1	1	2	2	2	3	3	3	3	4	4	4	4	4	5	5	5	5	5	5	…
m	0	1	1	0	2	2	1	1	3	3	0	2	2	4	4	1	1	3	3	5	5	…

where n, m, and j are the radial order, the azimuthal order and the polynomial index, respectively

Functions

filter

Surface filtering

gram_schmidt

Gram-schmidt ortho-normalization

gram_schmidt_with_dot

Gram-schmidt ortho-normalization with dot product function

jnm

Returns the Zernike indices (j,n,m) for the first n_radial_orders

mgs_mode_set

Orthonormal Zernike set

mgs_mode_set_on_mask

Orthonormal Zernike set

mode

Zernike mode on a regular grid n_xy X n_xy

mode_set

Zernike polynomial set

projection

Surface decomposition

projection_on_mask

Surface decomposition

zernike

Returns the Zernike polynomial (j,n,m) value at the polar coordinates (o,r)